Faculty of Education · Secondary School Mathematics Education · Undergraduate
Course Objective
Functions with one real variable are inadequate in formulating many problems, both in theory and in practice; many problems require controlling multiple variables. Therefore, the necessary infrastructure is needed to analyze functions with multiple variable numbers. To understand these structures, the analysis 3 courses will be taught.
Course Content
Functions of multiple variables; IRn's topology, limit, continuity, function series, and series; derivative, directional derivative, partial derivative, geometric interpretation of the partial derivative, higher-order derivatives, and chain rule.
Required Resources
1. Matematik Analiz, Mustafa Balcı,
2. Analiz, Mümin Yamankaradeniz, Uludağ Üniversitesi Basımevi, 1994.
3. Analize Giriş I- Diferansiyel Hesap, Mustafa Bayraktar, ISBN: 978-975-6355-34-3, 2007.
4. Thomas Calculus, George B. Thomas, Addison Wesley Press ISBN:0-201-75527-0.
Recommended Resources
5. Hüseyin Halilov, Alemdar Hasanoğlu, Mehmet Can, “Yüksek Matematik 1”, Literatür Yayınları, 1999.
6. B. Suer and H. Demir, “Freshman Calculus Book One Part Two”, METU Faculty of Arts and Sciences Pub., 1983.
7. Doç. Dr. Cevdet Cerit ve Prof. Dr. Ahmet Canoğlu, “Matematik Analiz 1,2”, İTÜ, 1991.Ders notları.
Course Learning Outcomes
- recognize the structure of multivariable functions
- have knowledge about topology of n-dimensional real spaces
- Learn the concept of limit and continuity in n-dimensional real spaces.
Core Area Distribution
Teaching Methods
Assessment & Evaluation
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 14 | 2 | 28 |
| Out of Class Study Period | 10 | 3 | 30 |
| Midterm | 2 | 5 | 10 |
| Quiz | 0 | 0 | 0 |
| Assignment | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 7 | 7 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Introduction to the course syllabus and multivariable functions | Essential source 1 |
| 2 | The topology of n-dimensional IR, | Essential source 1 |
| 3 | Domain and range of multivariable functions | Essential source 1 |
| 4 | Limit of n - dimensional R | Essential source 1 |
| 5 | Continuity in n dimensional real spaces | Essential source 1 |
| 6 | Partial Derivative | Essential source 1 |
| 7 | Happy October 29th Republic Day | Essential Source 1 |
| 8 | Midterm | Midterm |
| 9 | Higher-order derivatives | Essential source 1 |
| 10 | Chain Rule and Differentiability | Essential source 1 |
| 11 | Derivative of an implicit function | Essential source 1 |
| 12 | directional derivative | Essential source 1 |
| 13 | series | Essential source 1 |
| 14 | series | Essential source 1 |
| 15 | Final Exam | Final Exam |
| 16 |